Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.1: Poster
Thursday, March 27, 2003, 15:30–18:00, P1
State transformations on a heterogeneous quantum network by global control — •Friedemann Tonner and Günter Mahler — Institut für Theoretische Physik I, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
We demonstrate how an unknown heterogeneous quantum network—in general thought to be of rather limited use—can be turned into a substrate for unitary state transformations. The heterogeneity of the network allows to achieve this goal by means of time dependent variation of some global potential.
We consider a one-particle Hamilton model Ĥ in an n-dimensional Hilbert space Hn. Whether two states couple at all (Hij ≠ 0) is defined by the structure of a two-dimensional honeycomb lattice. Heterogeneity is introduced by choosing the couplings Hij (i ≤ j) randomly (i.e., each pair-Hamiltonian is taken from the Gaussian unitary ensemble).
The system is controlled only by a global offset potential u(t): Ĥ(t)=Ĥ+u(t) 1 for each time t in the interval [0,T]. A genetic algorithm varies u(t) to optimize the fidelity F=|⟨ψf | ψ(t=T) ⟩|2 of the transformation of a prepared initial state | ψi ⟩= | ψ(t=0) ⟩ into a state | ψ(t=T) ⟩ by measurement of the target state | ψf ⟩ at time t=T. By this method we achieve fidelities F ≥ 0.8 in a system of N=32 states.